Symmetry Limitations to Polarization of Polycrystalline Ferroelectrics

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Abstract
The general integral for the determination of the average resultant polarization P̄ in the direction of the applied polarizing electric field is evaluated under the assumption that the spontaneous polarization vector of each crystallite is limited to a highly symmetric set of directions. With the further assumption that a ferroelectric crystal has a structure which is a slight distortion of a nonpolar structure, expressions for P̄ are given which may be applied to any set of allowed polarization directions which is likely to occur; each of the 22 nonpolar crystal classes yields one such expression. The special cases of interest for each of the 10 polar classes are evaluated. A general expression for P̄ as a function of electric field strength is obtained and used to determine hysteresis curves for several commonly occurring special cases. The angular distribution of polarization vectors after complete polarization is also discussed for these special cases.